Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909654336929792 |
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| author | Di Matteo, Gianmichele Lamm, Tobias |
| author_facet | Di Matteo, Gianmichele Lamm, Tobias |
| contents | Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,α}$-regularity result for a sequence of such maps in the limit $p \searrow n$, assuming a uniform $n$-energy bound on its elements. The method of the proof follows the exact same lines as in \cite{strz3} but we need to check uniformity of estimates not previously considered there. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets Di Matteo, Gianmichele Lamm, Tobias Analysis of PDEs Differential Geometry 35-XX, 49-XX, 53-XX Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,α}$-regularity result for a sequence of such maps in the limit $p \searrow n$, assuming a uniform $n$-energy bound on its elements. The method of the proof follows the exact same lines as in \cite{strz3} but we need to check uniformity of estimates not previously considered there. |
| title | Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets |
| topic | Analysis of PDEs Differential Geometry 35-XX, 49-XX, 53-XX |
| url | https://arxiv.org/abs/2506.17151 |